We see that our result on the GRB neutrino flux differs significantly from that by the IceCube Collaboration [1]}, [2]}. The reason for the difference is due to different choices of the time window between the
neutrino events and the associated GRBs.
In our analysis, we adopt a larger time range from a few days for TeV events [3]} to a few months for PeV events [4]}
by taking into account a
sizable Lorentz violation effect of neutrinos and anti-neutrinos,
whereas the constraints on the GRB neutrino flux proposed by the IceCube Collaboration are based on an assumption that GRB neutrinos should be detected in very close temporal coincidence with the associated GRBs within a few hundred seconds [1]}, [2]}.
In the combined linear fitting of TeV and PeV neutrinos [4]},
we also obtained an intrinsic time difference
between neutrino and photon emissions
as \(\Delta t_{\rm in} = (1.7 \pm 3.6) \times 10^3 ~\rm s\) .
Though we have little information about the intrinsic time difference,
\(\Delta t_{\rm in}\)  of the order of 1-2 hour can be safely neglected in the
fittings of TeV and PeV neutrinos, since it is much more shorter than the
observed time differences of the order of days or even up to months.
